9 research outputs found
Proposal for a CFT interpretation of Watts' differential equation for percolation
G. M. T. Watts derived that in two dimensional critical percolation the
crossing probability Pi_hv satisfies a fifth order differential equation which
includes another one of third order whose independent solutions describe the
physically relevant quantities 1, Pi_h, Pi_hv.
We will show that this differential equation can be derived from a level
three null vector condition of a rational c=-24 CFT and motivate how this
solution may be fitted into known properties of percolation.Comment: LaTeX, 20p, added references, corrected typos and additional content
Note on SLE and logarithmic CFT
It is discussed how stochastic evolutions may be linked to logarithmic
conformal field theory. This introduces an extension of the stochastic Loewner
evolutions. Based on the existence of a logarithmic null vector in an
indecomposable highest-weight module of the Virasoro algebra, the
representation theory of the logarithmic conformal field theory is related to
entities conserved in mean under the stochastic process.Comment: 10 pages, LaTeX, v2: version to be publishe
SLE()and Boundary Coulomb Gas
We consider the coulomb gas model on the upper half plane with different
boundary conditions, namely Drichlet, Neuman and mixed. We related this model
to SLE() theories. We derive a set of conditions connecting the
total charge of the coulomb gas, the boundary charges, the parameters
and . Also we study a free fermion theory in presence of a boundary and
show with the same methods that it would lead to logarithmic boundary changing
operators.Comment: 10 pages, no figur